X₁₅₉₅

POINT CHELEB I

X₁₅₉₅ = midpoint of X₄ and X₁₅₉₃

5, 6, 7 3, 4, 5 Kepler Kimberling

X₁₅₉₅ (POINT CHELEB I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 1593}, {2, 3} (Euler line)

• Related Centers: X₄ (ORTHOCENTER), X₁₅₉₃ (POINT CEBALRAI), X₂ (CENTROID), X₃ (CIRCUMCENTER)

Trilinears: \(2 \sec A + \cos(B - C) : :\)

Search Value (6, 9, 13): \(-20.212829156298\)

▸ Incident Central Lines5 lines

{2, 3}, {33, 496}, {34, 495}, {39, 53}, {578, 1503}

▸ Functional Relations4 relations

• X₁₅₉₅ = midpoint of X₄ and X₁₅₉₃

• X₁₅₉₅ = inverse-in-orthocentroidal-circle of X₁₅₉₈

• X₁₅₉₅ = {X₄,X₅}-harmonic conjugate of X₁₅₉₆

• X₁₅₉₅ = X₃₂₉₅-of-orthic-triangle if ABC is acute

Notes

As a point on the Euler line, X₁₅₉₅ has Shinagawa coefficients \((F, 2E + F)\).